In Japanese Unexamined Patent Application Publication No. 2007-231959, a high pressure fuel pump is disclosed in which a compression chamber is formed by press-fitting a cup (called a plug in Japanese Unexamined Patent Application Publication No. 2007-231959) and a cylinder to an inner cylindrical surface (inner periphery) portion of a concave portion formed in a pump housing. In the high pressure fuel pump, the cylinder including the cup is pressure-fixed to the inner periphery of the pump housing by the screw thrust force of a cylinder holder. It is also stated that the cup and the cylinder may be integrally structured.